Company selection is used in most cases when you are a coach or consultant that is hiring for multiple customers.
Any employer can invite you to be a company manager or manager of a workspace for their company. You would then have access to post jobs and perform all the hiring steps for your customer within their company account.
In the company selection dropdown is where you select which company you are going to work in. Even if you have access to multiple companies, you will not be able to see jobs, workspaces, time logs etc for one company when you have selected another company.